In this paper we focus on the translation model defined by IBM
Model~4~\citep{model4}.  Translation using IBM Model~4 is performed by
treating the translation process a noisy-channel model where the
probability of the English sentence given a French sentence is,
$P(\mathbf{e}|\mathbf{f}) = P(\mathbf{f}|\mathbf{e}) \cdot
P(\mathbf{e})$, where $P(\mathbf{e}$) is a language model of English.
IBM Model~4 defines $P(\mathbf{f}|\mathbf{e})$ and models the
translation process as a generative process of how a sequence of
target words (in our case French or German) is generated from a
sequence of source words (English).

The generative story is as follows.  Imagine we have an English
sentence, $\mathbf{e} = e_1, \dots,e_l$ and along with a NULL word
($e_o$) and French sentence, $\mathbf{f} = f_1, \dots, f_m$.  First a
fertility is drawn for each English word (including the NULL symbol).
Then, for each $e_i$ we then independently draws a number of French
words equal to $e_i$'s fertility.  Finally we process the English
source tokens in sequence to determine the positions of their
generated French target words.  We refer the reader to~\cite{model4}
for full details.



%%% Local Variables: 
%%% mode: latex
%%% TeX-master: "ilp-mt"
%%% End: 
